Mr Miliband said Labour would lose "some millions of pounds" under his plan, although he admitted the political levy paid by millions of union members would continue, as would the current 'opt-out' arrangement which pertains to it.

"I value our link to the unions. It is part of what makes us rooted in our communities," he said.

"To exclude these people who want to be affiliated to the Labour would be wrong."

The move was not enough to placate the Conservatives, who quickly lashed out at the Labour leader.

Housing minister Grant Shapps told the BBC's Sunday Politics it was "one of the most disingenuous interviews I've seen all year".

The Conservative said Mr Miliband's offer was "a complete wheeze".

But analysis showed the proposals would actually cost Labour heavily in an election year, with the party set to lose £13 million on 2010 spending levels.

The Conservatives are wary of Mr Miliband taking the lead on a thorny issue, but they are also suspicious of the advantage handed to Labour by his compromise.

While the Miliband offer would cut off Labour from big union donations, it would still enjoy significant funds via the trade union membership levy – with the option of increasing the affiliation fee later.

For their part, the Tories rely on a small number of high-value donations which would all be capped at £5,000. Without the sort of mass-membership advantage Labour enjoys via its union links it could put the governing party at a significant disadvantage.